A TRANSITION TO ADVANCED MATHEMATICS helps you bridge the gap between calculus and advanced math courses. The most successful text of its kind, the 8th edition continues to provide a firm foundation in major concepts needed for continued study and guides you to think and express yourself mathematically to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors present introductions to modern algebra and analysis and place continuous emphasis throughout on improving your ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. You will come away with a solid intuition for the types of mathematical reasoning you ll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems. You will be exposed to a large number of examples and exercises that allow you to practice developing the skills needed to help them write and think like a mathematician.
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